Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• ISSN: 1815-0659
• Main Authors: Conway, T.O., Deift, P.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209516
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight / T.O. Conway, P. Deift // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 17 назв. — англ.

In this paper, we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight w(x)dx = log(2k/(1 - x))dx on (-1,1), with k > 1, and verify a conjecture of A. Magnus for these coefficients. We use Riemann-Hilbert/steepest-descent m...